ESCAPE PROBLEM FOR IRREVERSIBLE SYSTEMS

The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When this assumption fails many of the results of classical transition-rate theory no longer apply, and no general m ethod exists for computing the weak-noise asymptotic behavior of funda mental quantities such as the mean escape time. In this paper we prese nt a general technique for analyzing the weak-noise limit of a wide ra nge of stochastically perturbed continuous-time nonlinear dynamical sy stems. We simplify the original problem, which involves solving a part ial differential equation, into one in which only ordinary differentia l equations need be solved. This allows us to resolve some old issues for the case when detailed balance holds. When it does not hold, we sh ow how the formula for the asymptotic behavior of the mean escape time depends on the dynamics of the system along the most probable escape path. We also present results on short-time behavior and discuss the p ossibility of focusing along the escape path.